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Didymus rank-3 family: Difference between revisions

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= Euterpe =
= Euterpe =
Period: 1\1
Optimal ([[POTE]]) generators: ~3/2 = 696.1982, ~7/4 = 968.4280
EDO generators: [[12edo|(7, 10)\12]], [[14edo|(8, 11)\14]], [[31edo|(18, 25)\31]]
Scales:
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11
[[Comma list]]: 81/80, 99/98
[[Comma list]]: 81/80, 99/98
[[Mapping]]: [{{val| 1 0 -4 0 1 }}, {{val| 0 1 4 0 -2 }}, {{val| 0 0 0 1 2 }}]


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 9: Line 26:
: [[Eigenmonzo]]s: 2, 5, 7
: [[Eigenmonzo]]s: 2, 5, 7


[[Mapping]]: [{{val| 1 0 -4 0 1 }}, {{val| 0 1 4 0 -2 }}, {{val| 0 0 0 1 2 }}]
{{Val list|legend=1| 12, 17c, 19e, 26, 31, 88 }}


{{Val list|legend=1| 5, 12, 26, 31, 88 }}
[[Badness]]: 0.536 × 10<sup>-3</sup>


[[Badness]]: 0.536 × 10<sup>-3</sup>
</div></div>


= Calliope =
= Calliope =
[[Comma list]]: 81/80, 45/44
 
Period: 1\1
 
Optimal ([[POTE]]) generators: ~3/2 = 696.1982, ~7/4 = 968.4280
 
EDO generators: [[7edo|(4, 5)\7]], [[7edo|(4, 6)\7]], [[12edo|(7, 10)\12]]
 
Scales:
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7.11
 
[[Comma list]]: 45/44, 81/80
 
[[Mapping]]: [{{val| 1 0 -4 0 -6 }}, {{val| 0 1 4 0 6 }}, {{val| 0 0 0 1 0 }}]


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 23: Line 57:
: [[Eigenmonzo]]s: 2, 7/3, 11
: [[Eigenmonzo]]s: 2, 7/3, 11


[[Mapping]]: [{{val| 1 0 -4 0 -6 }}, {{val| 0 1 4 0 6 }}, {{val| 0 0 0 1 0 }}]
{{Val list|legend=1| 7d, 12, 19, 26, 45 }}
 
{{Val list|legend=1| 7, 12, 19, 26, 45 }}


[[Badness]]: 0.530 × 10<sup>-3</sup>
[[Badness]]: 0.530 × 10<sup>-3</sup>
</div></div>


= Erato =
= Erato =
Period: 1\1
Optimal ([[POTE]]) generators: ~3/2 = 696.4949, ~11/8 = 547.0252
EDO generators: [[12edo|(7, 6)\12]], [[19edo|(11, 9)\19]], [[31edo|(18, 14)\31]]
Scales:
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11
[[Comma list]]: 81/80, 126/125
[[Comma list]]: 81/80, 126/125


Line 37: Line 86:


[[Badness]]: 0.558 × 10<sup>-3</sup>
[[Badness]]: 0.558 × 10<sup>-3</sup>
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\1
Optimal ([[POTE]]) generators: ~3/2 = 695.9883, ~11/8 = 545.6817
EDO generators: [[12edo|(7, 6)\12]], [[19edo|(11, 9)\19]], [[31edo|(18, 14)\31]]
Scales:
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11.13
Comma list: 81/80, 105/104, 126/125
Comma list: 81/80, 105/104, 126/125


Line 44: Line 110:


{{Val list|legend=1| 12f, 19, 31, 50, 81 }}
{{Val list|legend=1| 12f, 19, 31, 50, 81 }}
</div></div>


= Clio =
= Clio =
Period: 1\1
Optimal ([[POTE]]) generators: ~3/2 = 697.2502, ~7/4 = 968.6295
EDO generators: [[7edo|(4, 6)\7]], [[12edo|(7, 10)\12]], [[31edo|(18, 25)\31]]
Scales:
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11
[[Comma list]]: 81/80, 176/175
[[Comma list]]: 81/80, 176/175


Line 55: Line 138:
Mapping: [{{val| 1 0 -4 0 -12 }}, {{val| 0 1 4 0 8 }}, {{val| 0 0 0 1 1 }}]
Mapping: [{{val| 1 0 -4 0 -12 }}, {{val| 0 1 4 0 8 }}, {{val| 0 0 0 1 1 }}]


{{Val list|legend=1| 7, 12, 24, 31, 105, 129 }}
{{Val list|legend=1| 7, 12, 19e, 24, 31, 105, 129 }}


Badness: 0.738 × 10<sup>-3</sup>
Badness: 0.738 × 10<sup>-3</sup>
</div></div>


= Polyhymnia =
= Polyhymnia =
Period: 1\1
Optimal ([[POTE]]) generators: ~3/2 = 696.2305, ~7/4 = 964.8695
EDO generators: [[7edo|(4, 6)\7]], [[19edo|(11, 15)\19]], [[31edo|(18, 25)\31]]
Scales:
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11
[[Comma list]]: 81/80, 385/384
[[Comma list]]: 81/80, 385/384


[[Mapping]]: [{{val| 1 0 -4 0 11 }}, {{val| 0 1 4 0 -3 }}, {{val| 0 0 0 1 -1 }}]
[[Mapping]]: [{{val| 1 0 -4 0 11 }}, {{val| 0 1 4 0 -3 }}, {{val| 0 0 0 1 -1 }}]


{{Val list|legend=1| 7, 19, 24, 26, 31, 38, 45 }}
{{Val list|legend=1| 7, 12e, 19, 24, 26, 31 }}
 
</div></div>


= Thalia =
= Thalia =
[[Comma list]]: 81/80, 55/54
 
Period: 1\1
 
Optimal ([[POTE]]) generators: ~3/2 = 692.0796, ~7/4 = 950.2565
 
EDO generators: [[5edo|(3, 4)\5]], [[7edo|(4, 5)\7]], [[7edo|(4, 6)\7]]
 
Scales:
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7.11
 
[[Comma list]]: 33/32, 55/54


[[Mapping]]: [{{val| 1 0 -4 0 5 }}, {{val| 0 1 4 0 -1 }}, {{val| 0 0 0 1 0 }}]
[[Mapping]]: [{{val| 1 0 -4 0 5 }}, {{val| 0 1 4 0 -1 }}, {{val| 0 0 0 1 0 }}]


{{Val list|legend=1| 5, 7, 12e, 19e }}
{{Val list|legend=1| 5, 7, 12e, 14c, 19e }}
 
</div></div>


= Melpomene =
= Melpomene =
Period: 1\1
Optimal ([[POTE]]) generators: ~3/2 = 699.2230, ~7/4 = 964.2363
EDO generators: [[5edo|(3, 4)\5]], [[7edo|(4, 5)\7]], [[12edo|(7, 10)\12]]
Scales:
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11
[[Comma list]]: 81/80, 56/55
[[Comma list]]: 81/80, 56/55


[[Mapping]]: [{{val| 1 0 -4 0 7 }}, {{val| 0 1 4 0 -4 }}, {{val| 0 0 0 1 1 }}]
[[Mapping]]: [{{val| 1 0 -4 0 7 }}, {{val| 0 1 4 0 -4 }}, {{val| 0 0 0 1 1 }}]


{{Val list|legend=1| 5, 12, 19, 24, 36 }}
{{Val list|legend=1| 7d, 12, 17c, 19, 24, 31e, 36 }}
 
</div></div>


= Urania =
= Urania =
Period: 1\1
Optimal ([[POTE]]) generators: ~11/9 = 348.0938, ~7/4 = 963.6042
EDO generators: [[7edo|(2, 5)\7]], [[14edo|(4, 11)\14]], [[31edo|(9, 25)\31]]
Scales: [[urania24]]
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11
[[Comma list]]: 81/80, 121/120
[[Comma list]]: 81/80, 121/120


Line 91: Line 242:
Map to lattice: [{{val| 0 2 8 0 5 }}, {{val| 0 0 0 -1 0 }}]
Map to lattice: [{{val| 0 2 8 0 5 }}, {{val| 0 0 0 -1 0 }}]


{{Val list|legend=1| 7, 14c, 24, 31, 100de, 131bde, 162bde }}
{{Val list|legend=1| 7, 14c, 17c, 24, 31, 100de, 131bde, 162bde }}


[[Badness]]: 0.842 × 10<sup>-3</sup>
[[Badness]]: 0.842 × 10<sup>-3</sup>
Line 97: Line 248:
[[Complexity spectrum]]: 11/9, 4/3, 12/11, 11/10, 10/9, 9/8, 11/8, 6/5, 5/4, 8/7, 7/6, 9/7, 14/11, 7/5
[[Complexity spectrum]]: 11/9, 4/3, 12/11, 11/10, 10/9, 9/8, 11/8, 6/5, 5/4, 8/7, 7/6, 9/7, 14/11, 7/5


Scale: [[urania24]]
</div></div>


= Terpsichore =
= Terpsichore =
Period: 1\1
Optimal ([[POTE]]) generators: ~3/2 = 696.2358, ~7/4 = 964.0006
EDO generators: [[14edo|(8, 11)\14]], [[19edo|(11, 8)\7]], [[31edo|(18, 25)\31]]
Scales:
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11
[[Comma list]]: 81/80, 540/539
[[Comma list]]: 81/80, 540/539


[[Mapping]]: [{{val| 1 0 -4 0 -2 }}, {{val| 0 1 4 0 7 }}, {{val| 0 0 0 1 -2 }}]
[[Mapping]]: [{{val| 1 0 -4 0 -2 }}, {{val| 0 1 4 0 7 }}, {{val| 0 0 0 1 -2 }}]


{{Val list|legend=1| 19, 31, 81, 112b }}
{{Val list|legend=1| 14c, 17c, 19, 31, 81, 112b }}


[[Badness]]: 0.850 × 10<sup>-3</sup>
[[Badness]]: 0.850 × 10<sup>-3</sup>


[[Complexity spectrum]]: 4/3, 10/9, 9/8, 6/5, 9/7, 7/5, 7/6, 5/4, 8/7, 11/9, 12/11, 11/8, 11/10, 14/11
[[Complexity spectrum]]: 4/3, 10/9, 9/8, 6/5, 9/7, 7/5, 7/6, 5/4, 8/7, 11/9, 12/11, 11/8, 11/10, 14/11
</div></div>


[[Category:Theory]]
[[Category:Theory]]
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